Determination of the optimum steady-state performance of an open-loop and a closed-loop valve-controlled hydro-motor drive: a design approach

Abstract

This article analyses the steady-state performance of an open-loop and a closed-loop proportional valve-controlled hydro-motor drive. The drives considered for the analysis consist of HSLT and LSHT hydro-motors. In this respect, considering the flow and torque losses of the valve and the hydro-motors, the system equations are deduced from the model. They are made non-dimensionalised, from where the expressions of the performance parameters in terms of the speed, efficiency and power transfer of the drives are determined. From the explicit design equations, the conditions for the maximum efficiency and the power transfer are obtained. The drives performances are analysed in both open-loop and closed-loop configurations and compared with the test data. Using the explicit design equations developed from the model, the effects of the losses of the hydro-motors and the control gain on the performance of the drives are studied. Using the simplified set of design equations developed in the model, the drive’s performance can be determined within its reasonable operating zone from a limited amount of test data.

Appendices

Appendix 1

1.1 Experimental setup

A schematic diagram of the test setup and the photographic view of the same are shown in Fig. 12. The main items are listed in Table 1 and their specifications are given in Table 2. A variable speed-driven fixed displacement pump (item no. 1) supplies pressurised fluid to the HSLT (HM1) and the LSHT (HM2) hydro-motors. The hydro-motors (item no. 7 and 8) in turn drive the loading pumps (item no. 9). The torque load on the motors was controlled by the set pressure adjustment of the proportional pressure relief valve (item no. 12). The signal voltage that varies from 0 to 10 V DC from the control panel (item no. 14) varies the flow rate through the valve supplied to the hydro-motors; thus, the variable speeds of the hydro-motors were obtained. At a time, one of the hydro-motors (HM1 or HM2) was connected with the pump supply. By regulating the flow control valve across the valve port, the effects of valve leakage on the performance of the hydro-motor drives were studied.

Fig. 12

The test setup. a Schematic diagram of the test setup. b Photograph of the test rig

Table 1 List of the components used in the test rig

Table 2 Summary of the major components and instruments used in the test setup

In determining the system’s performance, the supply pressure P _s , flow rate Q _s , the load pressure (P _l  = P₁–P₂), hydro-motor torque T _l , motor speed N _m , the supply and the return flow of the hydro-motors (Q₁ and Q₂) were measured by their respective sensors. By providing suitable water oil cooler, the viscosity of the fluid was kept reasonably constant during the experiment by maintaining oil temperature 50 ± 2 ^°C. The experiments were repeated several times to test the consistency of the responses before recording the data through data logger (Hydac Electronic GMBH, Operating Manual: Part No. 669855, Portable data Recorder HMG 3010, Edition 2012-06-28-V04 R01). The dynamic responses were obtained at the sampling rate of 10 ms.

Appendix 2

2.1 Determination of the loss coefficients

The characteristics of the external (R _lkg ) and the internal (R _ilkg ) leakage resistances of the HSLT hydro-motor are shown in Figs. 13 and 14, from where using Eq. 8, the equivalent leakage resistance (R_m1) is obtained and plotted in Fig. 15. The following equations obtained from Figs. 13, 14 and 15 express the nature of the resistances R _lkg , R _ilkg and R_m1:

$$R_{lkg} = a_{1} \times N_{m1} + c_{1} ,$$

(38)

where a₁ = 10⁹ and $c_{ 1} = - \; 4\times 10^{ 10} P_{1} + 6\times 10^{ 1 2} ,$

Fig. 13

Characteristics of the external leakage resistance (R_lkg) of the HSLT hydro-motor

Fig. 14

Characteristics of the internal leakage resistance (R_ilkg) of the HSLT hydro-motor

Fig. 15

Characteristics of the equivalent leakage resistance (R_m1) of the HSLT hydro-motor

$$R_{ilkg} = a_{2} \times N_{m1} + c_{2} ,$$

(39)

in which $a_{2} = - 3 \times 10^{10} P_{1} + 6 \times 10^{9} {\text{and}} c_{2} = - 10^{11} P_{1} + 2 \times 10^{12} ,$

$$R_{m1} = a_{3} \times N_{m3} + c_{3} ,$$

(40)

where $a_{3} = - \;2 \times 10^{7} P_{1} + 3 \times 10^{9} {\text{and}}\;c_{3} = - \;5 \times 10^{10} P_{1} + 7 \times 10^{12} .$

The equivalent leakage resistance (R_m2) of the LSHT hydro-motor is the same as its internal leakage resistance, as there is no external leakage port and its characteristics are given in Fig. 16.

Fig. 16

Characteristics of the equivalent leakage resistance (R_m2) of the LSHT hydro-motor

The following equation expresses the nature of the resistances R_m2.

$$R_{m2} = a_{4} N_{m2} + c_{4} ,$$

(41)

where $a_{4} = 3 \times 10^{6} P_{1} + 3 \times 10^{9} {\text{and}}\;c_{4} = - \;2 \times 10^{8} P_{1} + 7 \times 10^{11} .$

A sufficiently accurate representation of the torque characteristics of the HSLT hydro-motor shown in Fig. 17 is as follows:

Fig. 17

Torque characteristics of the HSLT hydro-motor

$$T_{l} = \, V_{m} \left( {P_{1} {-} \, P_{2} } \right){-}0.0038 \, N_{m} {-} \, 1.68.$$

(42)

Comparing Eq. 9, in Eq. 42, $V_{m} = {{0.0 7 7 6 5 {\text{ m}}^{ 3} } \mathord{\left/ {\vphantom {{0.0 7 7 6 5 {\text{ m}}^{ 3} } {{\text{rad }}R_{f} = \, 00. 3 8 {\text{ N s}}}}} \right. \kern-0pt} {{\text{rad }}R_{f} = \, 00. 3 8 {\text{ N s}}}}{{} \mathord{\left/ {\vphantom {{} {{\text{m and }}T_{c} = { 1}. 6 8 {\text{ N}}}}} \right. \kern-0pt} {{\text{m and }}T_{c} = { 1}. 6 8 {\text{ N}}}}.$

From Fig. 18, the the torque characteristics of the LSHT hydro-motor may be expressed as:

$$T_{l} = \, V_{m} \left( {P_{1} {-}P_{2} } \right){-}0.080 \, N_{m} {-}45.$$

(43)

Fig. 18

Torque characteristics of LSHT hydro-motor

As discussed in Eq. 42, comparing Eq. 9, in Eq. 35, V _m  = 1.583 m³/rad, R _f  = 0.080 N s/m and T _c  = 45 N.

In Eqs. 42 and 43, T_l, N _m and P are in N, rad/s and Nm², respectively.